A Projection-Based Approach to Bayesian Age Estimation under Stratigraphic Constraints

In archaeological chronology building, stratigraphic constraints arising from the excavation context are commonly incorporated into Bayesian models through order-constrained priors. However, these models suffer from well-documented artifacts: estimated durations are inflated, and the bias worsens as more samples are dated. First, we prove that this phenomenon is intrinsic to the prior: when all true ages coincide, the posterior duration converges to the prior support's width. We then propose an unconstrained posterior that does not include stratigraphic knowledge and project it onto the space induced by the stratigraphic order. The projected posterior is the Wasserstein-closest constrained distribution; it can be computed via isotonic regression on a directed acyclic graph and corrects duration inflation unlike constrained priors. Simulation studies and two archaeological case studies demonstrate substantial bias reduction and precision gains.